I think this would be a really cool feature. Imagine editing video and being able to add an updated h265 encoder
The logic must be very carefully implemented to allow over-writing only specific regions of the FPGA.
If you're re-flashing the entire logic array, it's pretty straightforward. If you want to leave some logic in and add an additional funcitonality, this is much more difficult.
This is really a limitaiton of the FPGA logic array implementation, not a linux shortcoming...